Levitated optomechanics, a new experimental physics platform, holds promise for fundamental science and quantum technological sensing applications. We demonstrate a simple and robust geometry for optical trapping in vacuum of a single nanoparticle based on a parabolic mirror and the optical gradient force. We demonstrate rapid parametric feedback cooling of all three motional degrees of freedom from room temperature to a few mK. A single laser at 1550nm, and a single photodiode, are used for trapping, position detection, and cooling for all three dimensions. Particles with diameters from 26nm to 160nm are trapped without feedback to 10 −5 mbar and with feedback-engaged the pressure is reduced to 10 −6 mbar. Modifications to the harmonic motion in the presence of noise and feedback are studied, and an experimental mechanical quality factor in excess of 4×10 7 is evaluated. This particle manipulation is key to build a nanoparticle matter-wave interferometer in order to test the quantum superposition principle in the macroscopic domain.

Levitated optomechanics is showing potential for precise force measurements. Here, we report a case study, to show experimentally the capacity of such a force sensor. Using an electric field as a tool to detect a Coulomb force applied onto a levitated nanosphere. We experimentally observe the spatial displacement of up to 6.6 nm of the levitated nanosphere by imposing a DC field. We further apply an AC field and demonstrate resonant enhancement of force sensing when a driving frequency, ωAC , and the frequency of the levitated mechanical oscillator, ω0, converge. We directly measure a force of 3.0 ± 1.5 × 10 −20 N with 10 second integration time, at a centre of mass temperature of 3 K and at a pressure of 1.6 × 10 −5 mbar.The ability to detect forces with increasing sensitivity, is of paramount importance for many fields of study, from detecting gravitational waves [1] to molecular force microscopy of cell structures and their dynamics [2]. In the case of a mechanical oscillator, the force sensitivity limit arises from the classical thermal noise, as given by,Where, k b is the Boltzmann constant, T is the temperature of the thermal environment, m, the mass of the object, ω 0 is the oscillator angular frequency, Q m = ω 0 /Γ 0 is the mechanical quality factor and Γ 0 is the damping factor. In recent decades, systems, such as cold-atoms traps, have pushed the boundaries of force sensitivities down to 1 × 10 [3,35]. The control of charges on nanoparticles is essential for experiments to prepare non-classical states of motion of the particle [30,36]. In addition, force detection at 1.63 × 10 −18 N/ √ Hz in levitated nanospheres has already been demonstrated [20] by experiment.Here, we take a detailed look at the interaction of an optically levitated dielectric charged particle with an external electric field as a case study for force sensing. We measure the effect of the Coulomb interaction on the motion of a single nanoparticle, at high vacuum (10 −5 mbar) by applying a DC and an AC electric field to a metallic needle positioned near the trapped particle. These particles can carry multiple elementary electric charges (e = 1.6 × 10 −19 C), and we use the Coulomb interaction to determine the number of elementary charges attached to the particle.The charge at the needle tip, q t , for a given applied voltage is according to Gauss's Law, s E·ds t = qt 0 , where s t is the surface of the needle tip, 0 is the vacuum permittivity, and E is the electric field. The electric field at any point in a potential, V , is given by −∇V = E. If, we approximate the needle tip as a sphere, of radius, r t , arXiv:1706.09774v3 [quant-ph]

We experimentally squeeze the thermal motional state of an optically levitated nanosphere, by fast switching between two trapping frequencies. The measured phase space distribution of the center-of-mass of our particle shows the typical shape of a squeezed thermal state, from which we infer up to 2.7 dB of squeezing along one motional direction. In these experiments the average thermal occupancy is high and even after squeezing the motional state remains in the remit of classical statistical mechanics. Nevertheless, we argue that the manipulation scheme described here could be used to achieve squeezing in the quantum regime, if preceded by cooling of the levitated mechanical oscillator. Additionally, a higher degree of squeezing could in principle be achieved by repeating the frequency-switching protocol multiple times.While squeezing a quantum state of light [1] has a long history of experiments, the squeezing of a massive mechanical harmonic oscillator has so far not seen many experimental realisations. The first demonstration of squeezing in a classical mechanical oscillator was by Rugar et.al [2]. Squeezing of classical motional states in electromechanical devices by parametric amplification and weak measurements has been subsequently proposed [3], and experimentally demonstrated in an optomechanical system [4]. Schemes relying on sinusoidal modulation of the spring constant have also been proposed and discussed by numerous authors [5][6][7][8]. In optomechanical cavities Genoni et al. suggested that squeezing below the ground-state fluctuations (quantum squeezing for brevity) may be attainable via continuous measurements and feedback [9]. Quantum squeezing of a high-frequency mechanical oscillator has only been experimentally demonstrated very recently, in a microwave optomechanical device [10,11]. Also only very recently a hybrid photonic-phononic waveguide device has shown the correlation properties of optomechanical two-mode squeezing [12]. Another interesting method of generating squeezing, of relevance to this Letter, relies on non-adiabatic shifts of the mechanical frequency. Such method was initially discussed in relation to light fields [13,14]. Similar ideas, utilising impulse kicks on a mechanical oscillator, have been discussed [15,16]. In this Letter we report the first experimental demonstration of mechanical squeezing via non-adiabatic frequency shifts, thus realising a useful tool to manipulate the state of a levitated optomechanical system.Theory-In what follows we shall present a quantum mechanical treatment of our squeezing protocol, in anticipation of future experiments that may achieve quantum squeezing. Due to linearity of the Heisenberg equations of our system, it should be pointed out that formally identical results may be obtained through classical statistical mechanics [17]. We consider a nanosphere of mass m trapped in a harmonic potential. Along the z axis, we can manipulate the system by switching between two HamiltoniansĤ 1 ,Ĥ 2 , whereĤ j =p 2 2m + 1 2 mω 2 jẑ 2 ,ẑ,p denote the...

We demonstrate a classical analogy to the Fano anti-resonance in levitated optomechanics by applying a DC electric field. Specifically, we experimentally tune the Fano parameter by applying a DC voltage from 0 kV to 10 kV on a nearby charged needle tip. We find consistent results across negative and positive needle voltages, with the Fano line-shape feature able to exist at both higher and lower frequencies than the fundamental oscillator frequency. We can use the Fano parameter to characterize our system to be sensitive to static interactions which are ever-present. Currently, we can distinguish a static Coulomb force of 2.7 ± 0.5 × 10 −15 N with the Fano parameter, which is measured with one second of integration time. Furthermore, we are able to extract the charge to mass ratio of the trapped nanoparticle.

No abstract